2. Alan and Bill agree (through a public exchange) on using the Diffie-Hellman a

Question

2. Alan and Bill agree (through a public exchange) on using the Diffie-Hellman algorithm to create a common secret key. They also agree on two public numbers: q (large prime number), a (generator mod q): q = 7, a = 2 Alan generates a random CA =6, use CA to calculate DA and then sends DA to Bill. Alan has also received a value DB from Bill. Bill generates a random CB =7, use CB to calculate DB and then sends DB to Alan. Bill has also received the value DA sent from Alan as mentioned above. (a) What is DA? (i.e. DA =?) (4 points) (b) What is DB? (i.e. DB =?) (4 points) (c) What is the common secret key between Alan and Bill? (4 points) (Note you must show calculation procedures to obtain full points for each question)

Explanation / Answer

Given :

q = 7

a = 2

Formula to find DA & DB:

^ ---- Find the power of succeeding value

mod ---- Find the modulo function and returns remainder value

DA = a^CA mod q = (2)6 mod 7 = 64 % 2 = 1

DB = a^CB mod q = (2)7 mod 7 = 128 % 7 = 2

Formula to find the secret key s:

s = DB^CA mod q = (2)6 mod 7 = 64 % 7 = 1

s = DA^CB mod q = (1)7 mod 7 = 1 % 7 = 1

Solution:

DA = 1

DB = 2

Secret Key = 1

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